False Negative is Type II error (also known as the error of excessive skepticism). It is also known as the oversight error - believing the premise (based on observations) when in fact it is false. Or in lawyer's terms ruling the defendant innocent when in fact he is guilty.
Last night I told the Trustees that "I was paid to be a skeptic on conversion dates". Excessive skepticism is viewed as counter productive, anti progress, and pessimistic attitude. There is a reason they use the term "Devils Advocate".
There is no right answer on which is worse - False Positives or False Negatives (the cynic or the gullible). Both can be solved with infinite sample sizes in statistics.
It's like politics - you need emphasis on both "False" errors - Republicans and Democrats :)
Or maybe you are experiencing TYPE III error - using the wrong null hypothesis (asking the wrong question).